Simplify (4 square root of 6)/( square root of 30)

$\frac{4 \sqrt{6}}{\sqrt{30}}$

Step 1

Combine $\sqrt{6}$ and $\sqrt{30}$ into a single radical.

$4 \sqrt{\frac{6}{30}}$

Step 2

Cancel the common factor of $6$ and $30$ .

Factor $6$ out of $6$ .

$4 \sqrt{\frac{6 (1)}{30}}$

Cancel the common factors.

Factor $6$ out of $30$ .

$4 \sqrt{\frac{6 \cdot 1}{6 \cdot 5}}$

Cancel the common factor.

$4 \sqrt{\frac{6 \cdot 1}{6 \cdot 5}}$

Rewrite the expression.

$4 \sqrt{\frac{1}{5}}$

Step 3

Rewrite $\sqrt{\frac{1}{5}}$ as $\frac{\sqrt{1}}{\sqrt{5}}$ .

$4 \frac{\sqrt{1}}{\sqrt{5}}$

Step 4

Any root of $1$ is $1$ .

$4 \frac{1}{\sqrt{5}}$

Step 5

Multiply $\frac{1}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$4 (\frac{1}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}})$

Step 6

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$4 \frac{\sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$4 \frac{\sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$4 \frac{\sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \frac{\sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$4 \frac{\sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$4 \frac{\sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \frac{\sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$4 \frac{\sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 \frac{\sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$4 \frac{\sqrt{5}}{5^{1}}$

Evaluate the exponent.

$4 \frac{\sqrt{5}}{5}$

Step 7

Combine $4$ and $\frac{\sqrt{5}}{5}$ .

$\frac{4 \sqrt{5}}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{5}}{5}$

Decimal Form:

$1.78885438 \dots$

Simplify (4 square root of 6)/( square root of 30)

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